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a
Indicate whether statement is true of false, if a plane contains one of the two skew lines, it contains the other.
a
Answer to Problem 1PSA
False, It will never contain the second skew line
Explanation of Solution
Given information:
A plane contains one of the two skew lines
Since, skew lines never intersect and are not parallel.
Hence, it will never contain the other
b
The following statement “The given line and given plane never meet, if they both are parallel” is true or not.
b
Answer to Problem 1PSA
True, The line and plane will never meet
Explanation of Solution
Given information:
The given and plane will never meet, if they are parallel
Parallel means never meet even on extension
c
Indicate whether statement is true of false, if two parallel lines are in different planes, the planes are parallel
c
Answer to Problem 1PSA
True but not always the given planes are parallel
Explanation of Solution
Given information:
Two lines are in different planes
Two planes are parallel, sometimes it parallel lines are lying in those planes
d
Indicate whether statement is true of false, the two planes are parallel, if a line is perpendicular to two planes.
d
Answer to Problem 1PSA
True, both the given planes will be parallel
Explanation of Solution
Given information:
A given line is perpendicular to two planes
The given line can be seen lying in two planes if both the given planes are parallel
e
Indicate whether statement is true of false, the given plane and line are parallel to each other, if a plane and a line not in the plane are each perpendicular to the same line
e
Answer to Problem 1PSA
True, they will be always parallel
Explanation of Solution
Given information:
The given plane and a line, not in the plane are each perpendicular to the same line parallel to each other
The given plane and a line which are not in the plane are each perpendicular to the same line is only possible when they are parallel to each other
Chapter 6 Solutions
Geometry For Enjoyment And Challenge
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